Search

As a nonlinear dynamic system, the dynamic equation of triboelectric nanogenerator system is not only difficult to accurately establish, but also difficult to solve. The output signals of triboelectric nanogenerator system depends on the initial conditions of the system, which reflects the dynamic behavior of the system. Currently, there is little research on using the output signals to study the dynamic behavior of triboelectric nanogenerator system. Therefore, a dynamic simulation model of a freestanding triboelectric nanogenerator (F-TENG) system was established using COMSOL software. The mathematical model of the F-TENG system was fitted. Using chaos theory and its phase-space reconstruction technology, the phase-space trajectories of the F-TENG system were reconstructed through voltage signals under external factors, and the dynamic behavior of the F-TENG system was discussed and studied. Finally, validation experiments were carried out. The research shows that with the variation of internal factors and operating frequency, the mathematical model of the F-TENG system remains basically unchanged, and the variation law of output characteristics also remains basically unchanged. The F-TENG system is in periodic motion; with the variation of external factors such as resistance and friction layer spacing, the mathematical model of the F-TENG system will evolve in a complex direction, and the output characteristics will gradually distort. The F-TENG system will evolve from periodic motion to chaotic motion. The research results not only reveal the dynamic behavior and enrich the nonlinear dynamic theory of triboelectric nanogenerator system, but also provide theoretical guidance for increasing the working bandwidth and stability of triboelectric nanogenerator system. [ABSTRACT FROM AUTHOR]

In this paper, the qualitative properties of a physically extended six-dimensional Lorenz system, with additional physical terms describing rotation and density, which was proposed in [Moon et al., 2019] have been investigated. The dissipation, invariance, Lyapunov exponents, Kaplan–Yorke dimension, ultimate boundedness and global attractivity of this six-dimensional Lorenz system have been discussed in detail according to the chaotic systems theory. We find that this system exhibits chaos phenomena for a new set of parameters. It is well known that the general method for studying the bounds of a chaotic system is to construct a suitable Lyapunov-like function (or the generalized positive definite and radically unbounded Lyapunov function). However, the higher the dimension of a chaotic system, the more difficult it is to construct the Lyapunov-like function. The innovation of this paper is that we first construct the suitable Lyapunov-like function for this six-dimensional Lorenz system, and then we prove that this system is not only globally bounded for varying parameters, but it also gives a collection of global absorbing sets for this system with respect to all parameters of this system according to Lyapunov's direct method and the optimization method. Furthermore, we obtain the rate of the trajectories going from the exterior to the global absorbing set. Some numerical simulations are presented to validate our research results. Finally, we give a direct application of the results obtained in this paper. According to the results of this paper, we can conclude that the equilibrium point O (0 , 0 , 0 , 0 , 0 , 0) of this system is globally exponentially stable. [ABSTRACT FROM AUTHOR]

One of the routine exercises to manage and improve the performance and utility of the cloud is the migration or transfer of cloud data whether it is large or small. However, it is extremely challenging to protect both data privacy and integrity concurrently while moving cloud data, particularly when it is very vast. Collectively, prior works fail to offer a complete solution to these problem. Even though data encryption and steganography techniques are popular and efficient, they provide higher time and space complexities and introduce information loss. As a result, the goal of this research is to provide a chaos compression and encryption system based on chaos theory to guarantee both data privacy and integrity during the transit or migration of massive cloud data. During data transmission, the entire data are compressed using a chaotic substitution box followed by an adaptive Huffman encoding algorithms. Therefore, the input data are efficiently transformed into a non-readable form which replaces the original data, making it difficult for an unethical individual or group to determine its true sense. Our evaluation results show that the proposed chaotic technique has a maximum entropy value of 7.99, which supports its ability to provide more privacy when compared to previous techniques. It also delivers the best bits per code of 4.41, a throughput of 2.89 MB/s, and a minimal information loss percentage of 0.0011%, demonstrating its superior time, space efficiency, and ability to improve data integrity over existing methods. [ABSTRACT FROM AUTHOR]

Background: This research delves into the complexity management of collaborative networks and interorganizational systems in the health innovation ecosystem on the basis of a best practice in the coronavirus disease 2019 (COVID-19) crisis. The objective is to offer specific solutions and guidelines to stakeholders in the health innovation ecosystem to control the chaos resulting from unexpected events along the ecosystem development and evolution path. Methods: For this purpose, the performance of the Health Innovation Ecosystem in Iran (the Every Home is a Health Base plan) has been examined through a detailed and in-depth analysis of events and actions taken using documents, reports and interviews with experts. The practical application of chaos and complex adaptive system features (adaptation, time horizons, edge of chaos, sensitivity to initial conditions, state space and strange attractors) is introduced to identify and manage the transition from a state where the health innovation ecosystem is on the edge of chaos and prone to failure. Data were collected through studying documents, reports and interviews with experts, and then analysed using qualitative content analysis techniques, open and axial coding and metaphors derived from complexity and chaos theories. Results: The findings indicate that to understand and embrace the complexity of the health innovation ecosystem throughout its development and evolution and manage and lead it through the edge of chaos towards successful interorganizational systems performance, it is necessary to use gap analysis to achieve consensus, establish a highly interactive governance structure with key stakeholders of the ecosystem, maintain flexibility to control bifurcations (butterfly effect), prevent transforming emergency solutions into standard routines and ensure the sustainability of the ecosystem against future threats by long-term financial security. Conclusions: This research provides insights into the dynamics of complex health systems and offers strategies for promoting successful innovation through collaborative networks and interorganizational systems in the development and evolution of the health innovation ecosystem. By embracing complexity and chaos, healthcare professionals, policy-makers and researchers can collaboratively address complex challenges and improve outcomes in health network activities. The conclusion section provides guidelines for successfully managing the complexity of the ecosystem and offers suggestions for further research. [ABSTRACT FROM AUTHOR]

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields. [ABSTRACT FROM AUTHOR]

Nowadays, establishing security in data transmission is essential, and it is achieved by cryptography. Encryption of still or video images in specific applications such as Internet of Things, medical and satellite imaging, in applications requiring high-speed encryption, or even in applications where a personal computer is unavailable or cannot be used needs special hardware. In this paper, an image encryption algorithm based on chaos theory named Parallel Chaotic Checksum-based Image Encryption or PCCIE algorithm is proposed that has been able to provide a fast, efficient and secure algorithm with a hardware perspective on the design and parallel system structure. Using high-level synthesis, PCCIE is implemented on a Field Programmable Gate Array (FPGA). The proposed algorithm using small and independent local image buffers solved FPGA internal memory limitation for encryption of large images. Ultimately, a Hexa-core crypto-processor with single-precision floating-point and fixed-point precision has been designed, capable of encrypting 256 × 256 and Full HD images in 2.13 and 59.52 milliseconds, respectively, at 469 and 16 frames per second. [ABSTRACT FROM AUTHOR]

The short-term traffic flow prediction can help to reduce flight delays and optimize resource allocation. Using chaos dynamics theory to analyze the chaotic characteristics of en-route traffic flow is the basis of short-term en-route traffic flow prediction and ensuring the orderly and smooth state of the en-route. This paper takes the time series of en-route traffic flow extracted from Automatic-Dependent Surveillance Broadcast (ADS-B) measured data as the research object, uses the improved C–C method to reconstruct the phase space, and uses the improved small data volume method to calculate the Lyapunov index to identify the chaos phenomenon of en-route traffic flow. In order to avoid the interference of chaos phenomenon on traffic prediction, the Wavelet Neural Network (WNN) model is established to predict the traffic flow at en-route points. The experimental shows that when the number of iterations is 10,000, the average accuracy of WNN prediction is 0.87173, and the average running time is 6.9335334 s. According to the experimental results, it can be seen that the smaller number of iterations has more advantages in running time, which greatly reduces the overall running time. At the same time, it indicates that appropriately increasing or reducing the number of iterations in this experiment has little effect on the results. [ABSTRACT FROM AUTHOR]

In order to solve the dynamic analysis and chaotic motion control problems of the current-mode-controlled Boost converter system, a state equation model in the continuous current mode is established. The evolutionary path of the periodic motion of the system through the doubling bifurcation to the chaotic motion is analyzed by the bifurcation diagram, Poincaré sections and phase portraits. Then, according to the fundamental principle of the resonant parametric perturbation (RPP) method, a controller is designed based on the model-free adaptive control (MFAC) method to output the perturbation amplitude, and the disturbance quantity is calculated according to the perturbation amplitude. By adding a small amplitude disturbance to the controllable parameter of the controlled system, the chaotic motion of the system is guided to expected periodic orbit. The advantage of this method is that no precise mathematical model (PMM) of the system is required. At the same time, the design of the controller is simple and easy to implement. [ABSTRACT FROM AUTHOR]

Nonlinear dynamical problems, characterized by unpredictable and chaotic changes among variables over time, pose unique challenges in understanding. This paper explores the coupled nonlinear (2+1)-dimensional complex modified Korteweg-de-Vries (cmKdV) equation-a fundamental equation in applied magnetism and nanophysics. The study focuses on dynamic behaviors, specifically examining bifurcations and equilibrium points leading to chaotic phenomena by introducing an external term to the system. Employing chaos theory, we showcase the chaotic tendencies of the perturbed dynamical system. Additionally, a sensitivity analysis using the Runge-Kutta method reveals the solution's stability under slight variations in initial conditions. Innovatively, the paper utilizes the planar dynamical system technique to construct various solitons within the governing model. This research provides novel insights into the behavior of the (2+1)-dimensional cmKdV equation and its applications in applied magnetism and nanophysics. [ABSTRACT FROM AUTHOR]

This article is a tribute to Oleksandr Mykolayovych Sharkovsky, a renowned mathematician and one of the founders of the mathematical concept of deterministic chaos. Sharkovsky's groundbreaking work, including his famous Sharkovsky theorem, has had a significant impact on the theory of dynamical systems. The article highlights Sharkovsky's early life, education, and career, as well as his contributions to the field of mathematics. It also mentions his achievements, such as publishing 10 monographs and over 250 research works, and receiving several prestigious awards. Sharkovsky's work continues to be influential in the study of nonlinear dynamics and chaos theory. [Extracted from the article]

Smartphones, digital cameras, and other imaging devices generate vast amounts of high-resolution colored images daily, stored on devices equipped with multi-core central processing units or on the cloud. Safeguarding these images from potential attackers has become a pressing concern. This paper introduces a set of six innovative image ciphers designed to be stronger, faster, and more efficient. Three of these algorithms incorporate the State-Based Tent Map (SBTM) Chaotic Pseudo Random Number Generator (CPRNG), while the remaining three employ a proposed modified variant, SBTMPi. The Grayscale Image Cipher (GIC), Colored Image Cipher Single-Thread RGB (CIC1), and Colored Image Cipher Three-Thread RGB (CIC3) showcase the application of the proposed algorithms. By incorporating novel techniques in the confusion and diffusion phases, these ciphers demonstrate remarkable performance, particularly with large colored images. The study underscores the potential of SBTM-based image ciphers, contributing to the advancement of secure image encryption techniques with robust random number generation capabilities. [ABSTRACT FROM AUTHOR]

Memristors have several chaotic dynamic models and have been used successfully in various fields, including secure communication systems, information storage, and artificial neural networks. The memristor-based four-dimensional chaotic (FDMC) systems generate unpredictable and intricate time domain signals. Parameter fluctuations in the FDMC system may give birth to chaos, making it difficult to suppress. Stabilizing chaos in the FDMC system improves the circuit's performance. This paper synthesizes a novel time-efficient chatter-free nonlinear robust adaptive control (NLRAC) technique that stabilizes chaos in the FDMC system affected by time-varying unknown bounded exogenous disturbances and model uncertainties. The proposed NLRAC strategy decimates the time-varying unknown bounded exogenous disturbances and model uncertainties effects; it establishes a faster, smoother state-variable trajectories convergence to the zero vicinity. The theoretical analysis and mathematical proofs are based on the Lyapunov stability technique. Computer simulation results show that the proposed NLRAC technique effectively brings the FDMC system's state-variable trajectories to zero with reduced fluctuations for control input signals and state-variable trajectories. This feedback controller's attribute enhances closed-loop stability performance, improves precision, and reduces risk overshoot. The paper includes comparative computer simulation results to endorse the proposed controller performance. [ABSTRACT FROM AUTHOR]

Metaheuristic techniques are capable of representing optimization frames with their specific theories as well as objective functions owing to their being adjustable and effective in various applications. Through the optimization of deep learning models, metaheuristic algorithms inspired by nature, imitating the behavior of living and non-living beings, have been used for about four decades to solve challenging, complex, and chaotic problems. These algorithms can be categorized as evolution-based, swarm-based, nature-based, human-based, hybrid, or chaos-based. Chaos theory, as a useful approach to understanding neural network optimization, has the basic idea of viewing the neural network optimization as a dynamical system in which the equation schemes are utilized from the space pertaining to learnable parameters, namely optimization trajectory, to itself, which enables the description of the evolution of the system by understanding the training behavior, which is to say the number of iterations over time. The examination of the recent studies reveals the importance of chaos theory, which is sensitive to initial conditions with randomness and dynamical properties that are principally emerging on the complex multimodal landscape. Chaotic optimization, in this regard, accelerates the speed of the algorithm while also enhancing the variety of movement patterns. The significance of hybrid algorithms developed through their applications in different domains concerning real-world phenomena and well-known benchmark problems in the literature is also evident. Metaheuristic optimization algorithms have also been applied to deep learning or deep neural networks (DNNs), a branch of machine learning. In this respect, the basic features of deep learning and DNNs and the extensive use of metaheuristic algorithms are overviewed and explained. Accordingly, the current review aims at providing new insights into the studies that deal with metaheuristic algorithms, hybrid-based metaheuristics, chaos-based metaheuristics as well as deep learning besides presenting recent information on the development of the essence of this branch of science with emerging opportunities, applicability-based optimization aspects and generation of well-informed decisions. [ABSTRACT FROM AUTHOR]

Thunderstorms endanger life and infrastructure. The accurate and precise prediction of thunderstorms is therefore helpful to enable protection measures and to reduce the risks. This manuscript presents the latest developments to improve thunderstorm forecasting in the first few hours. This includes the description and discussion of a new Julia-based method (JuliaTSnow) for the temporal extrapolation of thunderstorms and the blending of this method with the numerical weather prediction model (NWP) ICON. The combination of ICON and JuliaTSnow attempts to overcome the limitations associated with the pure extrapolation of observations with atmospheric motion vectors (AMVs) and thus increase the prediction horizon. For the blending, the operational ICON-D2 is used, but also the experimental ICON-RUC, which is implemented with a faster data assimilation update cycle. The blended products are evaluated against lightning data. The critical success index (CSI) for the blended RUC product is higher for all forecast time steps. This is mainly due to the higher resolution of the AMVs (prediction hours 0–2) and the rapid update cycle of ICON-RUC (prediction hours 2–6). The results demonstrate the potential of the rapid update cycle to improve the short-term forecasts of thunderstorms. Moreover, the transition between AMV-driven nowcasting to NWP is much smoother in the blended RUC product, which points to the advantages of fast data assimilation for seamless predictions. The CSI is well above the critical value of 0.5 for the 0–2 h forecasts. Values below 0.5 mean that the number of hits (correct informations) is lower than the number of failures, which results from the missed cells plus false alarms. The product is then no longer useful in forecasting thunderstorms with a spatial accuracy of 0.3 degrees. Unfortunately, with RUC, the CSI also drops below 0.5 when the last forecast is more than 3 h away from the last data assimilation, indicating the lack of model physics to accurately predict thunderstorms. This lack is simply a result of chaos theory. Within this context, the role of NWP in comparison with artificial intelligence (AI) is discussed, and it is concluded that AI could replace physical short-term forecasts in the near future. [ABSTRACT FROM AUTHOR]

This research presents a comprehensive investigation into the electromagnetic compatibility (EMC) analysis of rail vehicle speed sensors. It begins by establishing rigorous EMC testing standards for radio field speed sensors used in railway vehicles, encompassing parameters such as antenna orientation, interference strength, frequency range, and signal stability. Additionally, the study explores the theoretical underpinnings of radio frequency (RF) emissions, emphasizing the importance of loop size in PCBs with transmission lines and the complexities involved in estimating field strength. Notably, the research introduces the integration of quantum-based 3D reconstruction algorithms into EMC analysis, enabling a more accurate representation of the electromagnetic environment surrounding rail vehicles. Furthermore, an optimization algorithm based on chaos theory and neural networks is proposed, offering a promising approach to fine-tune sensor design for enhanced EMC compliance. Through experiments and tests, the study demonstrates the significant impact of optimization and quantum-enhanced 3D reconstruction on the EMC of rail vehicle speed sensors, resulting in reduced RF radiation and improved electromagnetic compatibility. This research contributes to the advancement of EMC analysis in the railway industry, ensuring the safety and performance of critical components. [ABSTRACT FROM AUTHOR]

Herringbone gear planetary gear transmission system has the advantages of high contact ratio and high bearing capacity and is widely used in various heavy load fields. However, the gear generates a large amount of heat during the meshing transmission, which affects the nonlinear dynamic characteristics of the system. In this paper, the various nonlinear factors are considered, including time-varying meshing stiffness, engagement damping, backlash, and engagement error. A nonlinear dynamic model of the herringbone planetary gear system considering temperature effects is established by using the lumped-parameter method. The nonlinear vibration differential equation of the system is solved by using the Runge–Kutta method. The impact law of temperature and engagement damping ratio changes on the bifurcation features of the herringbone planetary gear system is studied by combining the maximum Lyapunov exponent diagram, bifurcation diagram, time domain diagram, phase diagram, Poincare diagram, and spectrogram. And the chaos phenomenon of the system is analyzed and controlled by using a non-feedback control method with the external periodic signal. The result shows that with the change of temperature rise and meshing damping ratio, the system exhibits the kinematics response of chaotic, multi-period, and single-period. Higher temperature rise (∆T > 64 °C) and larger engagement damping ratio (ξ > 0.122) can make the gear system enter stable periodic motion. The chaotic motion region of the system is effectively controlled to the periodic motion orbit by introducing the periodic signal feedback controller. The relevant conclusions can provide a theoretical basis for the optimal design of the dynamic structure stability of herringbone planetary gear. [ABSTRACT FROM AUTHOR]

In recent times, there have been notable advancements in solar energy and other renewable sources, underscoring their vital contribution to environmental conservation. Solar cells play a crucial role in converting sunlight into electricity, providing a sustainable energy alternative. Despite their significance, effectively optimizing photovoltaic system parameters remains a challenge. To tackle this issue, this study introduces a new optimization approach based on the coati optimization algorithm (COA), which integrates opposition-based learning and chaos theory. Unlike existing methods, the COA aims to maximize power output by integrating solar system parameters efficiently. This strategy represents a significant improvement over traditional algorithms, as evidenced by experimental findings demonstrating improved parameter setting accuracy and a substantial increase in the Friedman rating. As global energy demand continues to rise due to industrial expansion and population growth, the importance of sustainable energy sources becomes increasingly evident. Solar energy, characterized by its renewable nature, presents a promising solution to combat environmental pollution and lessen dependence on fossil fuels. This research emphasizes the critical role of COA-based optimization in advancing solar energy utilization and underscores the necessity for ongoing development in this field. [ABSTRACT FROM AUTHOR]

Currently, immunotherapy is seen to be the most effective cancer treatment. This is especially true while treating chronic lymphocytic leukemia (CLL), a slow-growing B-lymphocyte neoplasm that gradually compromises the immune system. Mathematical modeling is acknowledged as a key technique for analyzing theoretical and practical challenges in this field of cancer research and others. We were inspired to develop a mathematical model because of its dearth in investigations of chemotherapy-induced immunotherapy for CLL. This study effort formulates the dynamics of lymphocytic leukemia utilizing fractional calculus to conceptualize the complex processes of this viral illness. The basic idea of fractional calculus has been shown using the Atangana–Baleanu framework. For the suggested model's chaotic and dynamic behavior, a new numerical approach is described. We inspect the stability and convergence of the suggested numerical technique in our work. The fluctuation of various system input elements has demonstrated the oscillatory and chaotic behavior of the system. Moreover, we have demonstrated how the suggested mechanism of lymphocytic leukemia infection is affected by fractional order. Through numerical simulations, the most important input parameters are emphasized, and the policymakers are given control intervention suggestions. [ABSTRACT FROM AUTHOR]

This paper proposes a new four-dimensional hyper-chaotic system capable of generating multi-wing chaotic attractors by introducing active magnetron memristors, multi-segmented square functions and trigonometric functions. The dynamical properties of this new hyper-chaotic system, such as equilibrium point, dissipation, Lyapunov exponential spectrum, bifurcation diagram and Poincaré cross-section and attraction basin, are analyzed theoretically and simulated numerically, and the complexity of this system with different parameters is analyzed. It is observed that this hyper-chaotic system has periodic, chaotic and hyper-chaotic variations with an infinite number of equilibria and coexisting attractors under different parameter conditions. The circuit simulation was performed using Multisim and the results obtained were consistent with the numerical analysis of the dynamics, and the chaotic circuit system is designed by FPGA to verify the realizability of the system. Finally, an image encryption algorithm is designed in conjunction with the DNA algorithm to enable a new system chaotic sequence for image encryption. The results show that the hyper-chaotic system has rich dynamical behavior and has high-security performance when applied to image encryption with strong chaotic key and plaintext sensitivity and large key space in image encryption. [ABSTRACT FROM AUTHOR]

Aims Patients with heart failure (HF) can exhibit kinesiophobia, an excessive, debilitating, and irrational fear of movement. This study aimed to enhance the understanding of kinesiophobia in patients with HF by analysing associations with the following variables: musculoskeletal pain, quality of life, quality of sleep, functional capacity, disability, frailty, sex, and age. Methods and results In this cross-sectional study, 107 participants were included, with ages ranging from 28 to 97 years (57% men, mean age 73.18 ± 12.68 years). Multiple regression analyses were performed with all variables, including polynomial regressions for variables with a non-linear relationship. Kinesiophobia was significantly correlated (P < 0.01) with musculoskeletal pain, quality of life, quality of sleep, functional capacity, disability, and being at risk of frailty, while age and sex were not statistically significant. Frailty disability and musculoskeletal pain intensity were variables linearly associated with kinesiophobia, while quality of sleep and disability had a non-linear relationship with kinesiophobia. Conclusion Kinesiophobia needs to be evaluated and better understood in patients with HF to improve physical activity and exercise adherence. This study found that musculoskeletal pain intensity, quality of sleep, disability, and frailty risk have a significant association with kinesiophobia in patients with HF. Our results suggest multi-dimensional associations of kinesiophobia in patients with HF, which require further examination and understanding. [ABSTRACT FROM AUTHOR]

With the rapid development of computer network technology, it is often necessary to collect weak signals to collect favorable information. The development of signal detection technology is ongoing; however, various issues arise during the detection process. These issues include low efficiency and a high signal noise threshold. However, many problems will be encountered in the process of detection. In order to solve these problems, the nonlinear chaos theory is introduced to detect signals, and the simulation experiments of weak pulse signals and weak partial discharge signals are carried out respectively. The experimental results showed that the detection effect was remarkable in the quasi periodic state, and it had a good detection effect for weak pulse signals. At a signal-to-noise ratio of - 25 dB, double coupling system, two-way ring coupling system, and single ring coupling system displayed detection success rates exceeding 98%. Meanwhile, the detection success rate of the strong coupling system was only 12%. Even at a noise signal ratio as low as - 40 dB, the dual coupling system still maintained a detection success rate above 80%. The simulation results of partial discharge signal detection showed that there was a high fluctuation only at 2 ms, and the rest was basically stable at about 0 V, indicating that the system had a strong suppression effect on Gaussian white noise. When comparing the simulation results of the detection of the new chaotic system and the double coupling system, it was found that the new chaotic system has a superior impact in detecting weakly attenuated partial discharge signals. Through analysis of the system's dynamic behavior, the research confirms its rich dynamic characteristics and sheds light on the reasons for phase state mutation and missed detection. The noise system is utilized for comparing the performance of various systems, with the goal of enhancing the system's detection capability. [ABSTRACT FROM AUTHOR]

Modeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large subset of the multidimensional parameter space, the return map of the voltage dynamics is an expanding Lorenz map, we analyze both chaotic and periodic behavior of the system and describe the complexity of spiking patterns fired by a neuron. This is achieved by using and extending some results from the theory of Lorenz-like and expanding Lorenz mappings. [ABSTRACT FROM AUTHOR]

Chaotic systems depict complex dynamics, thanks to their nonlinear behaviors. With recent studies on fractional-order nonlinear systems, it is deduced that fractional-order analysis of a chaotic system enriches its dynamic behavior. Therefore, the investigation of the chaotic behavior of a 4D memristive Chen system is aimed in this study by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Based on these analyses, two different fractional orders (i.e., q = 0.948 and q = 0.97) are determined where the 4D memristive system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the fractional-order memristive chaotic system on the equilibrium points. Then, control method results are obtained by both numerical simulations and different illustrative experiments of microcontroller-based realization. As expected, voltage outputs of the microcontroller-based realization are in good agreement with the time series of numerical simulations. [ABSTRACT FROM AUTHOR]

To research the special transmission system type of the multistage closed-loop gear system of the 3D braiding machine, a multi-degree of freedom nonlinear dynamic model was established by using the lumped mass method, taking into account parameters such as meshing stiffness, static transmission error, backlash, and meshing damping. To reduce the computational complexity, a gear system with 12 gears was selected and solved using the Runge-Kutta method. Using meshing frequency, backlash, and meshing damping ratio as control parameters, we analyzed the bifurcation and chaos of the system under different conditions through bifurcation diagrams. Simultaneously using sequence diagram, phase plane diagrams, Poincare maps, and FFT diagrams to accurately display the motion state of the system. The analysis results indicate that with the increase of meshing frequency and backlash, the system exhibits a range of motion states, such as period-one motion, multi-periodic motion, quasi-periodic motion, and chaotic motion. Meanwhile, increasing the damping ratio can effectively suppress the chaotic state of the gear system and also reduce the maximum vibration displacement of the gear system. [ABSTRACT FROM AUTHOR]

It is widely acknowledged that fluidelastic instability (FEI), among other mechanisms, is of the greatest concern in the flow-induced vibration (FIV) of tube bundles in steam generators and heat exchangers. A range of theoretical models have been developed for FEI analysis, and, in addition to the earliest semi-empirical Connors' model, the unsteady model, the quasi-steady model and the semi-analytical model are believed to be three advanced models predominant in the literature. The unsteady and the quasi-static models share the merits of having explicit fluid force expressions and ease of being implemented but require more experimental inputs, whereas the semi-analytical model requires fewer parameters due to its analytical nature but is hard, if not prohibitive, to derive explicit fluid force expressions. Since the fluid force formulations set in the core of development of FEI models, the understanding and in particular the implementation of the semi-analytical model has been impaired by the nonexistence of explicit fluid force expression. This issue becomes more profound in time-domain analysis whereby the simple harmonic assumption is discarded. Here we report a new semi-analytical time-domain (SATD) FEI model with explicit fluid force expressions. The new model allows a consistent frequency-domain stability analysis and more importantly a truly time-domain response analysis. The theory was validated by calculating linear stability thresholds of two typical tube array patterns and comparing against reported experimental data. We then present a nonlinear time-domain analysis of a single loosely-supported tube with piece-wise linear stiffness. The nonlinear and nonsmooth dynamics was probed in details by utilizing various techniques, playing an emphasis on characterizing and distinguishing the chaotic vibration. We found that the system follows a quasi-periodic route to chaos. Such an in-depth study of the nonlinear dynamics of tubes in crossflow has never been reported in the context of SATD model. Our results enrich the theory and provide a different approach for linear and nonlinear dynamics of tube bundles, which are essential for the subsequent fretting wear analysis. • A new formulation on semi-analytical time-domain model for fluidelastic instability of tube bundles. • The formulation has explicit fluid force expressions. • Linear frequency- and time-domain analysis are validated against available experimental and theoretical results. • Nonlinear dynamics behavior of a loosely-supported tube is probed based on the new formulation by using various techniques. • The route to chaos of the system is found through quasi-periodic to chaos. [ABSTRACT FROM AUTHOR]

Dynamic systems theory and complexity theory (DST/CT) is a framework explaining how complex systems change and adapt over time. In psychotherapy, DST/CT can be used to understand how a person's mental and emotional state changes during therapy incorporating higher levels of complexity. This study aimed to systematically review the variability of DST/CT methods applied in psychotherapy research. A primary studies search was conducted in the EBSCO and Web of Knowledge databases, extracting information about the analyzed DST/CT phenomena, employed mathematical methods to investigate these phenomena, descriptions of specified dynamic models, psychotherapy phenomena, and other information regarding studies with empirical data (e.g., measurement granularity). After screening 38,216 abstracts and 4,194 full texts, N = 41 studies published from 1990 to 2021 were identified. The employed methods typically included measures of dynamic complexity or chaoticity. Computational and simulation studies most often employed first-order ordinary differential equations and typically focused on describing the time evolution of client-therapist dyadic influences. Eligible studies with empirical data were usually based on case studies and focused on data with high time intensity of within-session dynamics. This review provides a descriptive synthesis of the current state of the proliferation of DST/CT methods in the psychotherapy research field. [ABSTRACT FROM AUTHOR]

In this paper, the Caputo fractional derivative is assumed to be the prey–predator model. In order to create Caputo fractional differential equations for the prey–predator model, a discretization process is first used. The fixed points of the model are categorized topologically. We identify requirements for the fixed points of the suggested prey–predator model's local asymptotic stability. We demonstrate analytically that, under specific parametric conditions, a fractional order prey–predator model supports both a Neimark–Sacker (NS) bifurcation and a Flip bifurcation. We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory. The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey–predator model. As the bifurcation parameter is increased, the system displays chaotic behavior. Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations, phase portraits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. The suggested prey–predator dynamical system's chaotic behavior will be controlled by the OGY and hybrid control methodology, which will also visualize the chaotic state for various biological parameters. [ABSTRACT FROM AUTHOR]

Electricity is an essential energy resource in the industrial, commercial and housing sector, having a very important role in the development of societies. Urbanization and industrialization implies a great demand of energy for developing economies. In the search to be able to know how much electrical energy is consumed, a modeling of the electrical energy demand is carried out. However, the inherent intricacy and nonlinear nature of electricity consumption patterns present a significant obstacle to achieve precise modeling. In this article, a chaos theory approach is carried out to analyze the behavior of the system and to obtain properties of its dynamic system. A network consisting of a convolutional part, a hidden part and an output part is proposed. Convolutional operations are employed for dimensionality reduction in transformed data sets by reconstruction of the phase space. A radial basis function neural is used in the hidden part. The dynamic analysis approach using chaos theory, and the proposed neural network is compared with the radial basis function neural network for the modeling of electrical energy consumption. [ABSTRACT FROM AUTHOR]

This article addresses this challenge and proposes a novel approach based on the modified cuckoo search and chaos theory. This article describes a novel approach for multilevel biomedical image segmentation based on the modified cuckoo search and chaos theory which is the major contribution to the literature. The modified cuckoo search approach helps to model the Lévy flight efficiently and the incorporation of the chaos theory helps to maintain the diversity in the population. The proposed approach helps to determine the optimal threshold values for a given number of thresholds. Four different objective functions are used to get the realistic segmented output which is essential in biomedical image analysis. Moreover, detailed analysis is also helpful in understanding the suitable objective function for biomedical image segmentation. This work also helps to choose suitable chaotic maps with different optimization algorithms. Hybridization of chaos theory and modified cuckoo search helps to overcome the local optima and to find the global optima cost-effectively. The chaos theory is incorporated in this proposed work to replace some solutions with some chaotic sequences to enhance the associated randomness with various phases which is beneficial to overcome the premature convergence and its related issues. The optimum setup is determined by investigating the effect of different chaotic maps along with some standard metaheuristic optimization approaches. Both qualitative and quantitative approaches are used to evaluate and compare the proposed approach. The proposed algorithm is compared with four state-of-the-art approaches. The obtained results clearly show that the proposed approach outperforms some state-of-the-art approaches in terms of both quantitative results and segmented output. On average, the proposed approach can achieve 255.8331 MSE, 24.07047 PSNR, 291.6077 mean, 0.038869 SD, 0.688655 SSIM, and 16.05358 s execution time (all for nine clusters). It can be observed that the proposed approach can determine the optimal set of clusters comparatively faster on most occasions, especially for the higher number of clusters. [ABSTRACT FROM AUTHOR]

One of the primary challenges in distributed systems, such as cloud computing, lies in ensuring that data objects are accessible within a reasonable timeframe. To address this challenge, the data objects are replicated across multiple servers. Estimating the minimum quantity of data replicas and their optimal placement is considered an NP-complete optimization problem. The primary objectives of the current research include minimizing data processing costs, reducing the quantity of replicas, and maximizing the applied algorithms’ reliability in replica placement. This paper introduces a hybrid chaos-based swarm approach using the modified shuffle-frog leaping algorithm with a new local search strategy for replicating data in distributed systems. Taking into account the algorithm’s performance in static settings, the introduced method reduces the expenses associated with replica placement. The results of the experiment conducted on a standard data set indicate that the proposed approach can decrease data access time by about 33% when using approximately seven replicas. When executed several times, the suggested method yields a standard deviation of approximately 0.012 for the results, which is lower than the result existing algorithms produce. Additionally, the new approach’s success rate is higher in comparison with existing algorithms used in addressing the problem of replica placement. [ABSTRACT FROM AUTHOR]

Home area network (HAN) devices send the electricity consumption and other important data to the smart meter that must remain confidential from other devices. This paper proposes a novel one-dimensional hybrid chaotic map. The proposed map shows excellent chaotic properties when analyzed by bifurcation diagram, Lyapunov exponent & Shannon entropy. We further design an encryption strategy for data transfers between the smart meter and HAN devices. The proposed encryption scheme uses the existing lightweight key management in advanced metering infrastructure (LKM-AMI) architecture for data transfers, in which the encrypted data is transferred through an insecure channel and private keys are provided by trusted third party (TTP) through secure channels. The 2-way communication between HAN devices and the smart meter sends messages that are encrypted by using the proposed novel hybrid one-dimensional chaotic map. The encryption strategy mainly consists of three steps. In the first step, the seed and the control parameters are initialized. The second phase generates two intermediate keys using the proposed hybrid chaotic map. In the last phase, we encrypt the message by applying permutation followed by diffusion using intermediate keys. The proposed encryption strategy is resistant to various attacks. [ABSTRACT FROM AUTHOR]

The flow properties of pellets or granules are crucial for further processing drug dosage forms. Optimal compression or filling of multiparticulate dosage forms into capsules is influenced by forces between discrete particles, which could be partially characterized by flow properties. Several techniques have been developed to examine flowability, including static and dynamic methods applying empirical studies and up-to-date chaos theory; however, the newest methods seem only to be powerful with the supplementation of empirical principles. Our experiments try to refine both the technique of analysis and the methods, by finding new, alternative ways. Our approach to the flowability measurements was to set up a dynamic time-dependent model that combined empirical observations and chaos theory on a geometrical basis, thus finding new characteristics regarding the flow properties of pellets and granules that could be relevant for drug developers. Our findings indicate that sphericity and particle size are the most significant factors influencing the flowability of pharmaceutical multiparticular preparations. Furthermore, this study confirms that integrating chaos theory and empirical observations in a time-dependent dynamic model provides a comprehensive understanding of particle flow behavior, pivotal for optimizing manufacturing processes. [ABSTRACT FROM AUTHOR]

Unpredictable strings are sequences of data with complex and erratic behavior, which makes them an object of interest in various scientific fields. Unpredictable strings related to chaos theory was investigated using a genetic algorithm. This paper presents a new genetic algorithm for converting large binary sequences into their periodic form. The MakePeriod method is also presented, which is aimed at optimizing the search for such periodic sequences, which significantly reduces the number of generations to achieve the result of the problem under consideration. The analysis of the deviation of a nonperiodic sequence from its considered periodic transformation was carried out, and methods of crossover and mutation were investigated. The proposed algorithm and its associated conclusions can be applied to processing large sequences and different values of the period, and also emphasize the importance of choosing the right methods of crossover and mutation when applying genetic algorithms to this task. [ABSTRACT FROM AUTHOR]

This study evaluated a pilot project designed to mentor clinical nurses using a formal program and ongoing support. [ABSTRACT FROM AUTHOR]

Many music therapists propose that chaos, such as destructiveness and disintegration, could thwart music therapy group processes and should be minimised or resolved. From a paradoxical approach, however, chaos is understood as a transformative complement to ordered, formative music therapy experiences. The research in this paper explored how music therapists and adolescents could engage with chaos as a resource in music therapy groups. From a paradoxical approach, the music therapist--researcher facilitated two short-term group music therapy processes with nine young South Africans from under-resourced and often violent communities, referred for committing offences. The researcher utilised crystallisation, including constructivist grounded theory, participatory action research, and abduction, to analyse how group members could engage with chaotic group experiences. Findings, constructed through a cyclical process of data collection, analysis, and inclusion of group feedback, are presented in a matrix. The matrix shows how groups could utilise chaos to explore multiple possibilities for responding to challenges. They expressed themselves courageously and played unconventional group roles through their musicking and participation. They juggled paradoxical tensions between observational and active, integrative and disintegrative, engagement styles. This supported their transformation in the group, and potentially within the chaotic South African context. Music therapists can use the matrix to support adolescents in music therapy groups to engage with chaos as a transformative resource. They can accompany young people through offering holding, resources and collaborative support. When it is safe, music therapists may allow or encourage chaos that empowers adolescents to cope with challenges independently. [ABSTRACT FROM AUTHOR]

• A wider class of homogeneous spacetimes can be described using General Relativity. • The models are categorized into Bianchi I to IX, by employing Lie Algebras. • We explore several inflationary Mixmaster models by using potential inflaton fields. • Inflation affects the stability of the Bianchi IX model, which becomes more stable. The objective of this research is to investigate the dynamical behavior of the Bianchi IX Universe through various inflationary models induced by scalar fields. Specifically, we explore potentials for the inflaton field of the form V (ϕ) ∝ ϕ δ , where c varies from 1 to 4. To discern any chaotic behavior in the system, we calculate basin diagrams using the smaller alignment index (SALI) and the grid classification method. The fractal nature of the basins is evaluated through the utilization of two distinct indicators, namely the box-counting dimension and the boundary basin entropy. Our findings reveal that the inflaton affects the stability of the Bianchi IX model, which is intrinsically chaotic and becomes more stable as the power of the scalar-field potential increases. Moreover, except in the case δ = 1 , the impact of the scalar field on the dynamics is independent of the exponent δ. [ABSTRACT FROM AUTHOR]

In the work, we prove the presence of chaotic dynamics, for suitable values of the model parameters, for the discrete-time system, composed of two coupled logistic maps, as formulated in Yousefi et al. [Discrete Dyn. Nat. Soc. 5, 161–177 (2000)], which describes two interdependent economies, characterized by two competitive markets each, with a demand link between them. In particular, we rely on the SAP (Stretching Along the Paths) method, based on a stretching relation for maps defined on sets homeomorphic to the unit square and expanding the paths along one direction. Such technique is topological in nature and allows to establish the existence of a semiconjugacy between the considered dynamical system and the Bernoulli shift, so that the main features related to the chaos of the latter (e.g., the positivity of the topological entropy) are transmitted to the former. In more detail, we apply the SAP method both to the first and to the second iterate of the map associated with our system, and we show how dealing with the second iterate, although being more demanding in terms of computations, allows for a larger freedom in the sign and in the variation range of the linking parameters for which chaos emerges. Moreover, the latter choice guarantees a good agreement with the numerical simulations, which highlight the presence of a chaotic attractor under the conditions derived for the applicability of the SAP technique to the second iterate of the map. [ABSTRACT FROM AUTHOR]

Prey–predator interactions are perhaps the most ordinarily noticed phenomena in the environment. In this article, we have proposed a three-species prey–predator model incorporating three important factors, namely, prey refuge, group defense, and the growth rate of two prey species which is reduced for the amount of fear of the predator species. All the biological parameters of our system have been presented as fuzzy numbers to make them more realistic. The system has been studied analytically and numerically in the fuzzy sense. Model analyses such as positivity, boundedness, and permanence of the system are investigated. Stability analysis at all equilibrium points of the system has been studied. Hopf bifurcation analysis around the positive interior equilibrium point has been discussed. All the numerical simulations of the system are presented with suitable tables and graphical diagrams by using MATHEMATICA and MATLAB. Numerically, we have seen that the fear effect and prey refuge parameter can stabilize the system from chaos to a stable region. The effect of fear and prey refuge on stability has been analyzed in the numerical section. Stable focus and limit cycle analysis are investigated in crisp as well as fuzzy environment. The system undergoes Hopf bifurcation at the positive equilibrium point when the fear parameter k and refuge parameter m cross the threshold value in crisp as well as fuzzy environment. [ABSTRACT FROM AUTHOR]

This paper explores a predator–prey system featuring fear and disease within the predator population,utilizing the Rosenzweig–MacArthur model with Holling type-II functional response. The primary focus lies in investigating the impact of a fear factor, wherein the prey's growth rate is hindered due to predator-induced fear. Additionally, the model accounts for the spread of disease among predators,leading to a division between susceptible and infected predator subpopulations. The inclusion of an Allee effect in the susceptible predator further enriches the model. The study involves a thorough examination, encompassing local and global stability analysis as well as Hopf bifurcation analysis around the interior equilibrium point. Numerical simulations underscore a noteworthy observation: an escalation in interaction force propels the system into chaotic dynamics,marked by stable focus, limit cycles and period-doubling phenomena. A noteworthy finding pertains to the influence of the Allee parameter (θ) on chaotic dynamics. As the Allee parameter values increase, the system tends to stable focus through a sequence of chaotic states, period-doubling and limit cycles. Subsequently, the paper introduces the role of another pivotal parameter, the fear factor, into the chaotic dynamics. Intriguingly, chaos transforms into stable focus through diverse nonlinear phenomena, including period-doubling and limit cycles. This nuanced exploration of parameters sheds light on the intricate dynamics governing the predator–prey system, offering a comprehensive understanding of the interplay between fear, disease and ecological factors. So our observation throughout this paper that how chaos behaves here after one by one injection of our new features: fear factor and Allee parameter? [ABSTRACT FROM AUTHOR]

In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaotic system characterized by only quadratic nonlinearities. We conducted an extensive analysis of this system's dynamical properties, encompassing the examination of equilibrium stability, bifurcation phenomena, Lyapunov analysis, and the system's basin of attraction. Our investigations revealed the presence of eight unstable equilibria, the coexistence of symmetrical strange repeller(s), and the potential for multistability in the system. [ABSTRACT FROM AUTHOR]

Stamping is a very important manufacturing process. To optimize the process parameters, a hybrid surrogate model based on the back-propagation neural network and sparse auto-encoder is proposed and compared with classical surrogate models to verify its reliability. Furthermore, the hybrid improved particle swarm optimization–genetic algorithm, based on chaos theory, is proposed and compared with other algorithms. A double-C part is used as an engineering example to verify the proposed method. The Latin hypercube sampling method is used for sampling and the response value is obtained by AutoForm simulation software. On this basis, the hybrid surrogate model is used to establish the mapping relationship between the forming quality of the double-C part and the stamping process parameters. The optimal stamping process parameters are obtained through the improved hybrid algorithm. The results demonstrate that the wrinkling of the optimized double-C part is significantly reduced and the forming quality is improved. [ABSTRACT FROM AUTHOR]

The rapid evolution of network technologies, where computer vision and the Internet seamlessly merge, poses significant challenges in safeguarding end-user data. To address the growing need for secure data in smart environments, lightweight and efficient security solutions are in high demand. Notably, the Trivium, a well-known encrypt stream cipher (eSTREAM) project, has been the target of several attacks. This paper proposes an innovative approach for fast and highly secured image encryption using byte scrambling and a modified version of the Trivium algorithm. The Henon map is utilized to generate random numbers for permutation, reducing time and increasing security. Performance is measured on 100 colour images with different several tests. The results present a fast and robust security system for the transmission process. It is more efficient than the traditional Trivium method. The encrypted-decryption time is reduced by 1:24 times, making it a quick security system for surgical telepresence and multimedia visuals. [ABSTRACT FROM AUTHOR]

Based on the structure of damaged bearing, a nonlinear dynamic model is proposed. The nonlinear vibration response is obtained by solving the dynamic equation of the bearing system. Firstly, the influence of radial load and rotational speed on the nonlinear vibration response of the bearing system is analyzed. Then, the different vibration characteristics of the system when the inner and outer raceways of the bearing are damaged are discussed. Finally, the influence of the degree of shaft current damage on the nonlinear characteristics of the bearing system is studied. The results indicate that the bearing system presents bifurcation, jump, and chaos with the change of radial load. With the increase of the rotational speed, the path of the bearing system from chaos to quasi-periodic changes. With the increase of the degree of shaft current damage, the system gradually transitions from a stable state to a chaotic state. [ABSTRACT FROM AUTHOR]

In order to effectively control the nonlinear dynamic response of the giant magnetostrictive actuator, a design scheme based on fractional-order time-delayed feedback control is proposed in this study. The J-A hysteresis nonlinear mathematical model of the GMA system is established considering the geometric nonlinearity introduced by the precompressed disc spring mechanism. On this basis, the amplitude-frequency response equation of the main resonance of the system under the fractional-order time-delayed feedback control strategy is solved using the averaging method, and the stability conditions of the system are determined based on the Routh-Hurwitz criterion. The influence of key structural parameters on the amplitude-frequency response characteristics of the GMA system is investigated by numerical simulation, and the laws of the main resonance peak and system stability with each time-delayed feedback parameter are obtained. Further, the influence of the excitation amplitude on the chaotic motion of the system is investigated by bifurcation diagram and Lyapunov exponential diagram. Finally, the chaotic motion of the system is suppressed by adjusting the time-delayed feedback gain and fractional order. The results show that the time-delayed feedback gain and fractional order have significant effects on suppressing the main resonance peak and the unstable region of the system, and can adjust the system response from chaotic motion to stable periodic motion, thus improving the stability of the system. [ABSTRACT FROM AUTHOR]

The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wide neural network of a single hidden layer, such as the error equation of Hopfield networks with respect to equilibria or visuo-motor tasks. It is shown that driving such systems with a certain amount of state-multiplicative noise, one can stabilize noise-free unstable systems. Linear-Matrix-Inequality-based stabilization conditions are derived, utilizing a novel non-quadratic Lyapunov functional and a numerical example where state-multiplicative noise stabilizes a nonlinear system exhibiting chaotic behavior is demonstrated. [ABSTRACT FROM AUTHOR]

In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc.) of the asymptotic laws and of convergence rates were studied. However, for basically all applications, e.g., for computer simulations, development of algorithms to study chaotic dynamical systems numerically, as well as for design and analysis of real (e.g., in physics) experiments, the exact values (or at least estimates) of constants (parameters) of the functions, which appear in the asymptotic laws and rates of convergence, are of primary interest. In this paper, we provide such estimates of constants (parameters) in the central limit theorem, large deviations principle, law of large numbers and the rate of correlations decay for strongly chaotic dynamical systems. [ABSTRACT FROM AUTHOR]

The objectives of this study are to: (1) develop an approach for extracting representative information from dam behaviour data and (2) diagnose deformation and crack opening behaviour by integrating techniques in transfer entropy (TE), chaos theory and wavelet transform (WT). First, TE is employed to map the information flow between measuring points to select the representative measuring point. The phase space reconstruction of observation data on dam behaviour is implemented, where lag time τ and embedding dimension m are identified by the statistical C–C method. The non-linear structural dynamical behaviour of the dam is then quantified in the form of the largest Lyapunov exponent representing system chaoticity. In addition, a moving window formula is employed to scan along the observation data to ensure an on-line continuous diagnosis. WT may be employed to assist in detecting the time where significant changes occur. A simple 4 degrees of freedom spring-mass-damper (K-M-C) system is employed to illustrate the performance of the proposed approach. The approach is then applied to an actual dam using monitoring data. From the deformation and crack opening behaviour, it is concluded that the studied dam is performing with no significant changes in behaviour over time. Transfer entropy is applied to map the information flow between measuring points. The representative information on structural behaviour of an actual dam is identified. TE and chaos theory are combined to diagnose the dam behaviour. A moving window is adopted to facilitate online statistical diagnosis. [ABSTRACT FROM AUTHOR]